Course: Calculus I

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Course title Calculus I
Course code KMA/MA1
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study 1
Semester Winter
Number of ECTS credits 8
Language of instruction Czech
Status of course Compulsory
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
  • Petrášková Vladimíra, doc. RNDr. Ph.D.
  • Kobera Marek, Mgr. Bc. Ph.D.
Course content
1. The concept of function. Basic properties of real-valued functions of one real variable. The composition of functions. Inverse functions. 2. Logarithmic function, exponential function, power function 3. Goniometrical functions, circular functions. 4. A limit of a function (definition). A limit of function formed by arithmetic operations. A limit of a composite function. Inequality theorems. 5. Continuity of a function in a point, over an interval. 6. Supremum and infimum of a set of real numbers. The theorem of monotone function limit. 7. Derivative of function at the point. Derivative of function formed by arithmetic operations. Derivative of composite function. 8. The mean value theorem - Rolle´s Theorem, Lagrange´s Theorem, Cauchy´s Theorem. Monotonic function at the point. 9. Absolute extreme of function. Monotonic function over the interval. 10. Relative extreme, necessary and sufficient condition. L´Hospital´s Rule. 11. Application. 12. Higher-order derivative. Convex and concave function over the interval. 13. Convex function at the point, concave function at the point. Inflection point. Asymptote. 14. Application.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming)
Learning outcomes
Classical analysis and differential calculus for the one variable function: limits, derivatives, continuity. Continuity of a function over an interval. L´Hospital rule, the course of a function.
The student will have a good grasp of basic terms concerning real-valued function of one real variable and a good grasp of the elements of differential calculus of the function of one variable.
Prerequisites
none

Assessment methods and criteria
Combined exam

active participation in colleges and tutorials, 2 successful written tests during the semester, elaborated homework
Recommended literature
  • Černý , I. :. Diferenciální a integrální počet 1 , Liberec , Technická univerzita , 1997.
  • Děmidovič , B. P. :. Sbornik zadač i upražněnij po matematičeskomu analizu , Moskva , Nauka , 1966.
  • Frolíková , J. :. Matematická analýza pro učitelské studium I.semestr , Praha , SPN , 1984.
  • Grossmann,S.,I.:. Calculus, Saunders College Publishing, 2001. Liberec, 1997.
  • Jarník , V. :. Diferenciální počet I , Praha , Academia , 1974.
  • Petrášková,V., Zmeškalová, E.:. Algebraické funkce, PF JU, Č.Budějovice 2005.
  • Zmeškalová, E., Petrášková,V.:. Poslopnosti, PF JU, Č.Budějovice 1999.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter